1,1,2,3,5,8...The Golden Ratio

Educational Goal: The Goal of this Lesson is to introduce the mathematical concept of the Golden Ratio to middle and high school age students. In this beginning lesson, the Golden Ratio will be introduced by showing it’s occurence throughout nature.

Students will be able to connect the Golden Ratio to direct natural objects they might see in their everyday life. This book can compliment the student's math and science curriculum.

Perceptual Options: Students are offered a variety of visual representations using computer images, photos, and correlating animations. All these visual aids help provide clear and diverse multiple representations of the Golden Ratio.

Linguistic Options: Recorded audio, audio scaffolding (Pedro, Hali and Monty), and computer text-to-speech options provide a variety of linguistic options from which the student can choose from.

Cognitive Learning Methods:The golden ratio concept is matched to student's prior knowledge of nature. This type of matching boosts each student’s working memory. Questions asked throughout the book demonstrate inquiry based instruction, using ‘self generated’ learning methods to increase students interest and attention.

The repetition and repeating visuals of the golden ratio help store the lesson in the student’s long term memory and working memory. Identifying similarities and differences in of the golden ratio throughout nature allows students to consider and remember what was learned. Clarifying animations assist in keeping students’ sustained engagement.

Assessment: Reflection and review at the conclusion allow the student to retain what they have learned. Students are encouraged to continue research about the golden ratio.

Applications to Neuroscience Research: The concept of the Golden Ratio is also supported by developmental cognitive researchers and neuroscientists like Kristy VanMarle, PhD. She currently researches whether humans perceive geometric figures that bear this ratio as more aesthetically pleasing than figures which bear different ratios.

In one of her current studies she is “trying to learn if babies (who cannot have had much experience with the Golden Ratio) prefer it over other "non-golden" ratios. In our task, babies are shown two rectangles, side-by-side, on computer monitors and we measure how long they look at each rectangle. For each pair of rectangles, one has the dimensions of a Golden Rectangle and one does not. If babies prefer the Golden Ratio, they are expected to look longer at Golden Rectangles than at non-golden rectangles. Evidence that babies prefer Golden Rectangles would suggest not only that this preference appears in humans, but also that it has an innate basis.”

About the Golden Ratio:The Golden Ratio can be illustrated within special dimensions of Sprials, Triangles and Rectangles where the ratio of the length of the short side to the long side is.618, was noted by ancient Greek architects as the most visually pleasing rectangle and its dimensions were used to construct buildings such as the Parthenon.